The Fourth Age: Total War is a Middle-earth modification; technically it cannot be called a LotR mod, because there is no Lord of the Rings (and no rings) anymore, this being the Fourth Age and all. The mod is based on one of Tolkien's unfinished tales, 'The New Shadow', but we draw on all the works of Tolkien for information and inspiration.

The Fourth Age: Total War and The Lord of the Rings: Total War are two completely different mods; the first a total conversion focusing on the full single player experience, made by a team of people based solely on the written works of J.R.R. Tolkien; the second a mod made by one man, wlesmana, focusing (for the moment, at least) on single player custom battles and multiplayer, with no campaign. It is also based on Peter Jackson's adaptation of Tolkien's book, and not on the book itself.

wlesmana is a part of the FA:TW Mod Team, but no work has been shared between the mods because of their difference in nature, so the similarities must come from the fact that both mods share the same foundation - the works of Tolkien. Myself, I don't see very many similarities, other than the fact that both mods look great ;)

Apoc